Question: Rewrite as a simplified fraction. ${0.1\overline{2} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 12.2222...\\ 10x &= 1.2222...\end{align*}}$ Subtracting the two equations, we have: ${90x = 11}$ ${x = \dfrac{11}{90}} $